# Graph neural networks for simulating crack coalescence and propagation in brittle materials

**Authors:** Roberto Perera, Davide Guzzetti, Vinamra Agrawal  
**arXiv:** [2107.05142](https://arxiv.org/abs/2107.05142)  
**Date:** 2021-07-11  
**Summary page:** https://www.summarizepaper.com/en/paper/2107.05142v5/

## Key points

- Challenge of computationally expensive fracture mechanics simulations in brittle materials with multiple microcracks
- Physics-based models become inefficient and time-consuming as number of microcracks increases
- Proposal of a novel approach using a Graph Neural Network (GNN) based framework
- GNN framework trained on dataset generated by XFEM-based fracture simulator
- High prediction accuracy achieved on test set compared to XFEM-based simulator
- First prediction stage determines Mode-I and Mode-II stress intensity factors for stress evolution using LEFM
- Second prediction stage identifies which microcracks will propagate
- Third stage propagates crack-tip positions for selected microcracks to next time instant
- GNN framework can simulate crack propagation, coalescence, and stress distribution for various initial microcrack configurations without modification
- Remarkable speed-ups in simulation time compared to XFEM-based simulator (6x to 25x faster)
- Improvement in efficiency crucial for practical applications requiring quick results

## Summary

This study addresses the challenge of computationally expensive fracture mechanics simulations in brittle materials with multiple microcracks. As the number of microcracks increases, physics-based models become inefficient and time-consuming. To overcome this limitation, the researchers propose a novel approach using a Graph Neural Network (GNN) based framework. The GNN framework is trained on a dataset generated by an XFEM-based fracture simulator. By engineering a sequence of GNN-based predictions, the framework achieves high prediction accuracy on the test set compared to the XFEM-based simulator. The first prediction stage determines Mode-I and Mode-II stress intensity factors, which are crucial for computing stress evolution using Linear Elastic Fracture Mechanics (LEFM). In the second prediction stage, the framework identifies which microcracks will propagate. Finally, in the third stage, crack-tip positions for selected microcracks are propagated to the next time instant. One significant advantage of this GNN framework is its ability to simulate crack propagation, coalescence, and corresponding stress distribution for various initial microcrack configurations ranging from 5 to 19 microcracks without any additional modification. This capability makes it an attractive approach for simulating microcrack propagation and stress evolution in brittle materials with multiple initial microcracks. Furthermore, compared to an XFEM-based simulator, the GNN framework demonstrates remarkable speed-ups in simulation time, ranging from 6x to 25x faster. This improvement in efficiency is crucial for practical applications where quick results are required. In summary, this research presents a promising solution to address computational challenges in fracture mechanics simulations involving multiple microcracks. The proposed GNN framework offers accurate predictions and efficient simulations while accommodating various initial microcrack configurations.